How do you export an STL using proper units?
The STL exporter has the Scale setting. You can use it to scale blender unit to one, that your target software uses. It's easy to find out exporting the default cube (2 x 2 x 2 meters), and check its size in the target software. Then use the coefficient found. As for display units, when you select 'Metric' in the scene's Units section, it gives the Scale setting enabled, where you can tell blender that one blender unit equals say 10 meters instead of default 1.
Note that you have to keep the scene scale adequate for blender's physics to work right. It assumes that 1 blender unit equals 1 meter.